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A fourth grade class of 28 students is given a standardized math test. The mean score of the 12 boys is 25 with a standard deviation of 3. The mean score of the 16 girls is 24 with a standard deviation of 4. What is the standard error for the sampling distribution

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Answer:

The standard error for the sampling distribution is 1.323.

Explanation:

Let X = scores of girls and Y = scores of boys.

The information provided is:


\bar x=24\\s_(x)=4\\n_(x)=16\\\bar y=25\\s_(y)=3\\n_(y)=12

As the population standard deviations are not known, use a pooled standard deviation to estimate the standard error of the sampling distribution.

The formula of pooled standard deviation is:


S_(p)=\sqrt{(s_(x)^(2))/(n_(x)^(2))+(s_(y)^(2))/(n_(y)^(2))}

Compute the standard error for the sampling distribution as follows:


SE=\sqrt{(s_(x)^(2))/(n_(x)^(2))+(s_(y)^(2))/(n_(y)^(2))}=\sqrt{(4^(2))/(16)+(3^(2))/(12)}=\sqrt{1+(9)/(12)}=\sqrt{(21)/(12)}=1.323

Thus, the standard error for the sampling distribution is 1.323.

User Jazuly
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